Question

The function y=−0.04x2+0.32x+2.5 represents the path of an Olympic swimmer as he enters the pool. x represents the distance, in feet, from the side of the pool and y represents the height of the swimmer, in feet, above the pool. The side of the pool is represented by x=0

Use the quadratic formula to determine how far from the side of the pool the swimmer enters the water.



x=−b±b2−4ac−−−−−−√2a

Answer 1

12.86 feet

Explanation:

For quadratic ax² +bx +c = 0, the quadratic formula gives the solutions as ...

`x=(-b\pm√(b^2-4ac))/(2a)`

When y=0, your equation has ...

a = -0.04, b=0.32, c=2.5

so the solutions will be ...

`x=(-0.32\pm√(0.32^2-4(-0.04)(2.5)))/(2(-0.04))\\\\=(-0.32\pm√(0.5024))/(-0.08)=4\pm√(78.5)`

The positive answer is the one of interest:

x ≈ 12.86 . . . feet

The swimmer enters the water about 12.86 feet from the side of the pool.